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Frank wrote:

" When you drop a pencil, it accelerates downward, but if you observe it in a 
freefall frame of reference (which is the modern definition of an inertial 
frame of reference) it does not accelerate at all. "

You brought up "freefall frame of reference" and I have some experience with 
freefall frames of reference since I have been in them 329 times after 
jumping out of airplanes. When you skydive, you normally face the earth after 
you leave the aircraft but sometimes you arrange your body position so that 
you look up at the airplane to look for the jumpers who are following you 
out. When you are in this freefall frame of reference, looking at the 
airplane, you, as the observer, observe the airplane accelerating upward at a 
rate of ten meters per second per second, getting very small very fast. Once 
you have made this observation you realize that there must be a force to 
explain the upward acceleration of the airplane that you just observed. Since 
F = MA and A =F/M we can calculate this force. If, for example, the airplane 
has a mass of one thousand kilograms then the force that caused the plane to 
accelerate upward must be ten thousand Newtons and I was able to create this 
force merely by stepping out of the plane. If I had jumped out of a Boeing 
727 (like D.B Cooper did) which has a mass of about 100,000 kilograms then 
the force to cause it to accelerate upward after I stepped out would be one 
million Newtons. (I find it interesting that I can take the same action, 
stepping outside, and create such great differences in forces just depending 
upon the mass of the plane.)

Since I have described this force maybe I will get credit for it and it will 
be named the "LaPook Force" in similar fashion to the Coriolis Force.

(Of course it might come as a surprise to the pilot that he is accelerating 
upward since his altimeter continues to show him maintaining altitude. It 
would also surprise the air traffic controller since he also sees the 
altitude readout on his radar scope staying constant.) 

Let's look at a different accelerating frame of reference. You are driving 
your car down the highway at seventy miles an hour. You suddenly crash into a 
tree. You now find yourself strapped into a frame of reference undergoing a 
rapid acceleration (say fifty Gs)in the direction that you had been coming 
from (decelerating.) You then observe your brother-in-law, Charlie, who had 
been sitting in the backseat, not using his seat belt, suddenly fly past you, 
smash through the windshield, and go skittering on down the road. You say to 
yourself that there must be some force to account for the fifty G 
acceleration that you just observed Charlie undergo. Charlie has a mass of 
one hundred kilograms so you calculate that the force on Charlie must have 
been 50,000 Newtons. Since you don't remember hearing this acceleration 
discussed in your physics class you decide to write up a description of it 
and, modestly, decide to name it, not after yourself, the "Charlie Force" in 
memory of your dear departed brother-in-law. 

It appears to me that the "LaPook Force" and the "Charlie Force" are just as 
valid as the "Coriolis Force."

gl







frankreed@HistoricalAtlas.com wrote:
> Sorry to be replying two weeks late to this message. I was travelling for much of August.
>
> John Huth (email apacherunner), you wrote:
> "The term "fictitious force" is intended to imply that it is an apparent 
force that arises in an accelerating frame of reference, whereas such a force 
does not exist in an inertial (i.e. non-accelerating) frame.   For this 
reason, I refer to this as the "Coriolis effect", as opposed to "Coriolis 
force", to avoid confusion."
>
>
> And yet, it's a force like any other so long as you use it correctly. 
Myself, I generally refer to it as the "Coriolis acceleration" since, like 
gravity, it is an acceleration field and these only fit into the framework of 
Newtonian "forces" if we adopt the "fiction" that they are defined by forces 
which are proportional to the object's own mass. While Coriolis and 
centrifugal accelerations are frame-dependent, this makes them no less "real" 
than local gravity itself. When you drop a pencil, it accelerates downward, 
but if you observe it in a freefall frame of reference (which is the modern 
definition of an inertial frame of reference) it does not accelerate at all. 
Rotating frames of reference are widely used in physics, and the suggestion 
that they are something to be avoided (not from you, but from a couple of 
other folks) is misleading. Of course, accelerated frames of reference have 
also been widely and infamously abused in an almost endless number of popular 
accounts of physics which undoubtedly explains some of the frustration that 
people feel when discussing these forces.
>
> And you wrote:
> "It is certainly true that you can express the Coriolis effect as an 
effective force if you are in a rotating frame of reference."
>
> And a great many phenomena in physics are readily understood by reference to 
centrifugal and coriolis forces which are rather more difficult to understand 
in inertial frames of reference, to put it mildly. 
>  
> I wrote previously:
> "The Coriolis acceleration is frame-dependent --it depends on the choice of 
a rotating frame of reference. It's intriguing to note that there is also an 
extremely tiny physical, non-frame-dependent, version of the Coriolis 
acceleration which is created by spinning masses. This is known as 
"frame-dragging" or "gravito-magnetism" and was measured (barely due to 
various problems with the ultra-sensitive gyroscopes) by a spacecraft known 
as "Gravity Probe B": http://einstein.stanford.edu/highlights/status1.html."
>
> And John, you replied:
> "I would be careful in separating the frame dragging effect, which is a 
result of general relativity from the classic Coriolis effect. Although they 
both result from the rotation of a mass, frame dragging only comes from 
general relativity and is a very small effect."
>
> Yes. And it is, as I said, "extremely tiny"... In any case, the important 
point here is that there is an exact correspondence between the relationship 
between the static gravitational force and centrifugal force, on the one 
hand, and the gravitomagnetic gravitational force and coriolis force, on the 
other. In much the same way that the centrifugal force in the rotating frame 
attached to the Earth is inseparable from static gravitation and leads us to 
say that the acceleration of gravity varies with latitude in both direction 
and magnitude, so also the Coriolis acceleration is modified by the dynamic 
gravitomagnetic field of the Earth in an inseparable fashion. The 
gravitomagnetic field is a physical, non-frame-dependent field which behaves 
exactly like a position-dependent version of the Coriolis acceleration. 
Finally, though this correspondence exists, the big difference (huge 
difference!) is that the gravitomagnetic field of the Earth is so tiny that 
it has barely been measured while the static gravitational field of the Earth 
is obviously all around us. [For anyone following along here, if you're 
wondering how you could go your whole life without hearing about this 
"gravitomagnetic field" thing, don't worry. You really can continue your 
whole life without thinking about it again unless it entertains you or 
enlightens you --it is a tiny and insignificant phenomenon. But it can be in 
fact very englightening so don't forget it too quickly... :-)].
>
> John, you added:
> "I'm not sure about why you say that the Coriolis effect has a deep 
connection to magnetism. Torque causing precession is happens in many 
systems.   I don't think you're suggesting that magnetic fields are the 
result of non-inertial frames, or are you?"
>
> No, not that of course. :-)
>
> First there is a simple classical physics connection. To see it, let's model 
a Foucault pendulum and a gyrocompass with equivalent electric and magnetic 
fields and with charges instead of masses. Let's assume that we are doing 
this experiment in freefall (no local gravity). For our pendulum we put a 
small plastic ball on the end of a string and hang it from the top of a large 
box. Large here means large compared to the amplitude of the swinging motion 
after we set the pendulum swinging. The string is just a bit shorter than the 
height of the box so that the ball can almost reach the base of the box. Put 
a small positive charge on that ball. The base of the box is a plastic sheet 
which we cover with a uniform negative charge. This creates a nearly uniform 
electric field above the base of the box. The ball on the string is attracted 
to it. If we give it a little push, it will starting swinging back and forth, 
and by selecting the correct charge density, we can get the pendulum swinging 
with just the right period to match any pendulum near the surface of the 
Earth. For the gyrocompass analogue, we make a spinning plastic wheel and 
hang it from the top of the box so that its center of mass is below its point 
of suspension, as is the case with a gyrocompass. On the rim of the wheel, we 
put some positive charge. Whether spinning or not, the wheel will be pulled 
by the static charge on the base of the box and it will hang "horizontally". 
So far, so good. We have an electrostatic model that corresponds to the 
static gravitational field. The pendulum swings back and forth. The gyro 
hangs horizontally.
>
> Now we need to add an equivalent to the Coriolis acceleration. To do this, 
we put our box inside a solenoid --a cylinder wrapped with current-carrying 
wire. This has a nearly constant magnetic field within the cylinder with the 
magnetic field vector aligned along the axis of the cylinder. The effect of 
this magnetic field is to deflect moving charges with an acceleration 
proportional to velocity and perpendicular to the plane containing the 
velocity vector and the axis of the cylinder and also proportional to the 
sine of the angle between the velocity and the axis of the cylinder. This is 
exactly analogous to the Coriolis acceleration where the axis of rotation of 
the frame of reference corresponds to the symmetry axis of the cylinder. The 
plane of the swing of the pendulum will now precess as the swinging charge is 
deflected by the magnetic field. Similarly, the gyroscope will precess about 
the direction of the magnetic field (though because it is hanging in the 
static electric field, it only nods back and forth around the direction of 
the axis of the cylinder. For even more fun, we can tilt the cylinder 
relative to the base of the box. The angular tilt corresponds to the tilt of 
the local gravitational surface with respect to the rotation of the Earth, or 
in other words, the tilt is the same as the observer's latitude on the Earth. 
And there we have it: a very nice electromagnetic analogue for phenomena in a 
gravitational field in a rotating frame of reference. But it must always be 
emphasized (can't do it enough!) that these are analogous systems. There are 
many similarities, some quite "profound", between gravitation and 
electromagnetism, but they are distinct force fields with different sources. 
And of course, electromagnetism is radically different from gravitational 
systems when we go beyond simple cases because EM charges can be positive, 
negative (or neutral).
>
> Note that the above electromagnetic model does not work merely because all 
torques and precession phenomena are similar. A constant magnetic field 
produces exactly the same motions on systems of charges (all assumed to have 
the same sign here) as a Coriolis acceleration field produces on systems of 
masses in a rotating frame of reference. See the PS below for a small 
difference...
>
> Beyond this classical analogy between constant magnetic fields and the 
accelerations in a rotating frame of reference, there is a more profound 
connection. Gravitation itself obeys Maxwell's equations (in the weak field, 
low velocity limit --no black holes, in other words). That is, the 
relationships which were discovered in the electromagnetic field in the 
nineteenth century have turned out to general properties and relationships of 
all field theories, primarily a ressult of local special relativistic 
transformation properties. Just as a current of flowing charge generates a 
field which deflects moving charges and causes current loops to precess near 
it, so a current of mass (a helluva lot of mass!) generates a similar field 
which deflects moving masses (any mass) and causes mass loops (gyros) to 
precess. This is the gravitomagnetic field. Unlike the common magnetic field, 
the gravitomagnetic field can be eliminated at any point by a suitable 
acceleration just as the static gravitational field can be eliminated at any 
point by working in a freefall frame of reference. But in this case, the 
elimination is done by rotation. The Coriolis acceleration nulls out the 
gravitomagnetic field at any point just as linear acceleration nulls out the 
static gravitational acceleration. I should emphasize that there is a lot 
more to this. It's not exactly "easy" either. For those among us who have 
studied some general relativity, a readable (but serious mathematical 
physics) account of some of this material can be found in "Gravitation and 
Inertia" by Ciufolini and the late, great John A. Wheeler.
>
> -FER
> PS: For completeness, I should add that the charges in this analogous system 
will produce some electromagnetic radiation which will damp out the motions 
much as air resistance (or other resistance) damps out the motion of a 
Foucault pendulum and also damps out the swinging of a gyrocompass until it 
falls rather quickly on true north. This EM radiation is a distinct 
difference from the gravitational case since gravitational radiation is many 
orders of magnitude weaker than EM radiation, and has, in fact, never been 
observed directly even from the brightest astronomical sources. 
>
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